Page 190 - Maths Skills - 7

188 Maths

A C B A

120°

120°
o o o o
C B B A A C B
120° C

Fig. (a) Fig. (b) Fig. (c) Fig. (d)

Order of Rotational Symmetry
The number of times a figure looks exactly the same as its original shape in a complete turn (rotation of 360°) is
called the order of rotational symmetry.
360°
Thus, Order of a rotational symmetry = .
Angle of rotation

ROTATION THROUGH 90° AND 180° FOR POLYGONS

Square
Draw a square ABCD and mark each angle with different
number as shown in Fig. (i). Locate its centre of rotation.
(Construct all the possible lines of symmetry.) Let it be
O. With OX as reference line, when the square ABCD is
rotated through 90°, the figure obtained would be Fig. (ii).
Similarly, when the figure is rotated through 180°, we will
obtain Fig. (iii).

Rectangle
Draw a rectangle ABCD and locate its centre of rotation O as shown in Fig (i). Let OX be the reference line.
Rotation through 90° will give the Fig. (ii), whereas rotation through 180° will give the Fig. (iii).

Similarly, other polygons can also be rotated through 90° and 180°. Try to rotate a pentagon and hexagon.

Rotational and Reflection Symmetry
We may find many 2D objects that show rotational as well as reflection symmetry. Some of
the examples are illustrated below.
A regular hexagon has six lines of symmetry and rotational symmetry of order six. It is
shown in fig. (a). Fig. (a)